Question

Three angles of a quadrilateral are equal. The fourth angle is twice one of the angles.

Find the measure of largest angle.

• A. ${144}^{\circ }$
• B. ${102}^{\circ }$
• C. ${70}^{\circ }$
• D. ${72}^{\circ }$

Answer 1

The correct option is A

${144}^{\circ }$

Let the measure of other equal angles be $x^{\circ }$.

Fourth angle = $2x^{\circ }$

The sum of all the angles of a quadrilateral is ${360}^{\circ }$.

$x^{\circ }+x^{\circ }+x^{\circ }+2x^{\circ }={360}^{\circ }$

$\Rightarrow 5x={360}^{\circ }$

$\Rightarrow x={72}^{\circ }$

Thus, the measure of the three equal angles is ${72}^{\circ }$.

Measure of fourth angle = $2x^{\circ }$ = ${144}^{\circ }$

Therefore, ${144}^{\circ }$ is the largest angle.